Gay, David T. (2021) Diffeomorphisms of the 4-sphere, Cerf theory and Montesinos twins. MPIM Preprint Series 2021 (7).
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Abstract
One way to better understand the smooth mapping class group of the 4-sphere would be to give a list of generators in the form of explicit diffeomorphisms supported in neighborhoods of submanifolds, in analogy with Dehn twists on surfaces. As a step in this direction, we describe a surjective homomorphism from a group associated to loops of 2-spheres in $S^2 \times S^2$’s onto this smooth mapping class group, discuss two natural and in some sense complementary subgroups of the domain of this homomomorphism, show that one is in the kernel, and give generators as above for the image of the other. These generators are described as twists along Montesinos twins, i.e. pairs of embedded 2-spheres in $S^4$ intersecting transversely at two points.
| Item Type: | MPIM Preprint |
|---|---|
| Subjects: | 3 Geometry and topology > 53-XX Differential geometry |
| Divisions: | Research > Preprints |
| Depositing User: | Andrea Kohlhuber |
| Date Deposited: | 31 Mar 2021 09:23 |
| Last Modified: | 18 May 2021 10:57 |
| URI: | https://archive.mpim-bonn.mpg.de/id/eprint/4525 |
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